Finite element mesh generation with blender
Well it is easy if you use existing librarys.
The greatest problem is generating a useful mesh for finite element analysis. In this case use the open source mesher "netgen" or "gmsh".
After generating the mesh there are several other openSource tools which can help you with subdomains and boundaries

----Fast manual solution ----
Export the blender file as an stl. 
Then import it in netgen and create a tetrahedral mesh.
After that use FreeCAD or CalculiX for labeling boundaries

---- Automatic solution ----
Use FreeCAD for the automatic import of the blender files and call netgen or gmsh.